Dialetheism
Dialetheism (
Dialetheism is not a
Motivations
Dialetheism resolves certain paradoxes
The
However, self-referential paradoxes, such as the Strengthened Liar can be avoided without revising the axioms by abandoning classical logic and accepting more than two truth values with the help of many-valued logic, such as fuzzy logic or Łukasiewicz logic.
Human reasoning
Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in the doorway to a room, it may seem reasonable both to affirm that John is in the room and to affirm that John is not in the room.
Critics argue that this merely reflects an ambiguity in our language rather than a dialetheic quality in our thoughts; if we replace the given statement with one that is less ambiguous (such as "John is halfway in the room" or "John is in the doorway"), the contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, the actual meaning of "being in the room" is not the same in both instances, and thus each sentence is not the exact logical negation of the other: therefore, they are not necessarily contradictory.
Moreover, John appears to be standing in a
Apparent dialetheism in other philosophical doctrines
The
The
Graham Priest argues in Beyond the Limits of Thought that dialetheia arise at the borders of expressibility, in a number of philosophical contexts other than formal semantics.
Formal consequences
In classical logics, taking a contradiction (see List of logic symbols) as a premise (that is, taking as a premise the truth of both and ), allows us to prove any statement . Indeed, since is true, the statement is true (by generalization). Taking together with is a disjunctive syllogism from which we can conclude . (This is often called the principle of explosion, since the truth of a contradiction is imagined to make the number of theorems in a system "explode".)[1]
Advantages
The proponents of dialetheism mainly advocate its ability to avoid problems faced by other more orthodox resolutions as a consequence of their appeals to hierarchies. According to Graham Priest, "the whole point of the dialetheic solution to the semantic paradoxes is to get rid of the distinction between object language and meta-language".[2] Another possibility is to utilize dialetheism along with a paraconsistent logic to resurrect the program of logicism advocated for by Frege and Russell.[8] This even allows one to prove the truth of otherwise unprovable theorems such as the well-ordering theorem and the falsity of others such as the continuum hypothesis.
There are also dialetheic solutions to the sorites paradox.
Criticisms
One criticism of dialetheism is that it fails to capture a crucial feature about negation, known as absoluteness of disagreement.[9]
Imagine John's utterance of P. Sally's typical way of disagreeing with John is a consequent utterance of ¬P. Yet, if we accept dialetheism, Sally's so uttering does not prevent her from also accepting P; after all, P may be a dialetheia and therefore it and its negation are both true. The absoluteness of disagreement is lost.
A response is that disagreement can be displayed by uttering "¬P and, furthermore, P is not a dialetheia". However, the most obvious codification of "P is not a dialetheia" is ¬(P ¬P). But this itself could be a dialetheia as well. One dialetheist response is to offer a distinction between
Absoluteness of disagreement is a powerful criticism that is not rescued by the ability to assert "this statement is not a dialetheia", as self-referential statements regarding dialetheia also prevent absoluteness in assertion, even regarding its own existence. P = "Dialetheia exist". I then assert that "P is a dialetheia".
See also
- Catuskoti
- Compossibility
- Doublethink
- Paraconsistent logic
- Problem of future contingents
- Subvaluationism
- Tetralemma
- Trivialism
References
- ^ a b Ben Burgis, Visiting Professor of Philosophy at the University of Ulsan in South Korea, in Blog&~Blog.
- ^ a b c Whittle, Bruno. "Dialetheism, Logical Consequence and Hierarchy." Analysis Vol. 64 Issue 4 (2004): 318–326.
- ^ Jc Beall in The Law of Non-Contradiction: New Philosophical Essays (Oxford: Oxford University Press, 2004), pp. 197–219.
- Review of Symbolic Logic3(1), 2010, pp. 71-92.
- ^ Matilal, Bimal Krishna. (1998), "The Character of Logic in India" (Albany, State University of New York Press), 127-139.
- ^ "Nagarjuna | Internet Encyclopedia of Philosophy".
- ^ Ganeri, J. (2002), "The Collected Essays of Bimal Krishna Matilal: Mind, Language and World" (Oxford University Press), 77-79.
- ^ Mortensen, Chris, "Inconsistent Mathematics", The Stanford Encyclopedia of Philosophy (Fall 2017 Edition), Edward N. Zalta (ed.).
- S2CID 195310673.
Sources
- Frege, Gottlob. "Negation." Logical Investigations. Trans. P. Geach and R. H Stoothoff. New Haven, Conn.: Yale University Press, 1977. 31–53.
- Parsons, Terence. "Assertion, Denial, and the Liar Paradox." Journal of Philosophical Logic 13 (1984): 137–152.
- Parsons, Terence. "True Contradictions." Canadian Journal of Philosophy 20 (1990): 335–354.
- Priest, Graham. In Contradiction. Dordrecht: Martinus Nijhoff (1987). (Second Edition, Oxford: Oxford University Press, 2006.)
- Priest, Graham. "What Is So Bad About Contradictions?" Journal of Philosophy 95 (1998): 410–426.
External links
- Berto, Francesco; Priest, Graham. "Dialetheism". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
- JC Beall UCONN Homepage
- (Blog & ~Blog)
- Paul Kabay on dialetheism and trivialism (includes both published and unpublished works)